Solve (8y^2) 2 -4(y-1)(12y-1)

Question

Simplify the expression

- 32 y^{2} + 52 y - 4

Show Solution

- 4 (8 y^{2} - 13 y + 1)

Show Solution

y_{1} = \frac{13 - 137}{16}, y_{2} = \frac{13 + 137}{16}

Alternative Form

y_{1} \approx 0.080956, y_{2} \approx 1.544044

Evaluate

(8 y^{2}) \times 2 - 4 (y - 1) (12 y - 1)

To find the roots of the expression,set the expression equal to 0

(8 y^{2}) \times 2 - 4 (y - 1) (12 y - 1) = 0

Multiply the terms

8 y^{2} \times 2 - 4 (y - 1) (12 y - 1) = 0

Multiply the numbers

16 y^{2} - 4 (y - 1) (12 y - 1) = 0

Calculate

More Steps

- 32 y^{2} + 52 y - 4 = 0

Multiply both sides

32 y^{2} - 52 y + 4 = 0

Substitute a= 32,b= - 52 and c= 4 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{52 \pm ( - 52 ) ^{2} - 4 \times 32 \times 4}{2 \times 32}

Simplify the expression

y = \frac{52 \pm ( - 52 ) ^{2} - 4 \times 32 \times 4}{64}

Simplify the expression

More Steps

y = \frac{52 \pm 2192}{64}

Simplify the radical expression

More Steps

y = \frac{52 \pm 4 137}{64}

Separate the equation into 2 possible cases

y = \frac{52 + 4 137}{64} y = \frac{52 - 4 137}{64}

Simplify the expression

More Steps

y = \frac{13 + 137}{16} y = \frac{52 - 4 137}{64}

Simplify the expression

More Steps

y = \frac{13 + 137}{16} y = \frac{13 - 137}{16}

Solution

y_{1} = \frac{13 - 137}{16}, y_{2} = \frac{13 + 137}{16}

Alternative Form

y_{1} \approx 0.080956, y_{2} \approx 1.544044

Show Solution